2D or 3D analytical models currently available in the literature are usually restricted to infinite regions. An original 2D-analytical model to calculate thermal cycles in regions of limited width using a vibrated/non-vibrated moving thermal source, has been developed here. First, the impact of the source size and then, the influence of the boundary on the thermal field within the limited region has been discussed. Finally, the model has been applied to electron beam welding and validated, concerning thermal kinetics, by comparison with experimental thermal cycles. (C) 2003 Elsevier Ltd. All rights reserved.